The Mathematics of Smoothed Particle Hydrodynamics (SPH) Consistency

被引：15

作者：

Sigalotti, Leonardo Di G. ^{[1
]}

Klapp, Jaime ^{[2
]}

Gesteira, Moncho Gomez ^{[3
]}

机构：

[1] Univ Autonoma Metropolitana Azcapotzalco, Dept Ciencias Bas, Area Fis Proc Irreversibles, Mexico City, DF, Mexico

[2] Inst Nacl Invest Nucl, Dept Fis, Ocoyoacac, Mexico

[3] Univ Vigo, Environm Phys Lab EPhysLab, CIM UVIGO, Edificio Campus Auga, Orense, Spain

来源：

FRONTIERS IN APPLIED MATHEMATICS AND STATISTICS | 2021年 / 7卷

基金：

欧盟地平线“2020”;

关键词：

particle methods; hydrodynamics; numerical integration; kernel consistency; particle consistency and convergence; error analysis and interval analysis; CONVERGENCE; KERNEL; COMPLETENESS; CONSERVATION; FORMULATION; IMPROVEMENT; ERROR; MESH;

D O I：

10.3389/fams.2021.797455

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Since its inception Smoothed Particle Hydrodynamics (SPH) has been widely employed as a numerical tool in different areas of science, engineering, and more recently in the animation of fluids for computer graphics applications. Although SPH is still in the process of experiencing continual theoretical and technical developments, the method has been improved over the years to overcome some shortcomings and deficiencies. Its widespread success is due to its simplicity, ease of implementation, and robustness in modeling complex systems. However, despite recent progress in consolidating its theoretical foundations, a long-standing key aspect of SPH is related to the loss of particle consistency, which affects its accuracy and convergence properties. In this paper, an overview of the mathematical aspects of the SPH consistency is presented with a focus on the most recent developments.

引用

页数：16

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